Abstract
This chapter reviews pictures that are treated as the graph-theoretic objects and introduces the graph theoretic. It defines the 2D and 3D adjacency graphs based on the grid point and grid cell models, and on the assumption that pixels and voxels are the smallest units (“atoms”) of a 2D or 3D grid. These graphs turn into the oriented adjacency graphs by specifying the local circular orders. Such graphs are related to the 2D combinatorial maps, which provide descriptions of the spatial subdivisions. Adjacencies are important in picture analysis at different levels of abstraction. Graphs provide representations of the relations and the tools for studying them. Two sub-graphs are disjoint if they have no nodes in common and such sub-graphs have no edges in common. This chapter concludes by reviewing two algorithms for component labeling in the pictures represented on the adjacency or incidence grids. These algorithms generalize to the component labeling in the arbitrary adjacency graphs.
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